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Despite the popularity of random forests (RF) as a prediction algorithm, methods for constructing confidence intervals for population means using this technique are still only sparsely reported. For two regional study areas (Spain and Norway) RF was used to predict forest volume or aboveground biomass using remotely sensed auxiliary data obtained from multiple sensors. Additionally, the changes per unit area of these forest attributes were estimated using indirect and direct methods. Multiple inferential frameworks have attracted increased recent attention for estimating the variances required for confidence intervals. For this study, three different statistical frameworks, design-based expansion, model-assisted and model-based estimators, were used for estimating population parameters and their variances. Pairs and wild bootstrapping approaches at different levels were compared for estimating the variances of the model-based estimates of the population means, as well as for mapping the uncertainty of the change predictions. The RF models accurately represented the relationship between the response and remotely sensed predictor variables, resulting in increased precision for estimates of the population means relative to design-based expansion estimates. Standard errors based on pairs bootstrapping within or internal to RF were considerably larger than standard errors based on both pairs and wild external bootstrapping of the entire RF algorithm. Pairs and wild external bootstrapping produced similar standard errors, but wild bootstrapping better mimicked the original structure of the sample data and better preserved the ranges of the predictor variables.

Estimating Forest Volume and Biomass and Their Changes Using Random Forests and Remotely Sensed Data